Problem: $\dfrac{ 7w + 7x }{ -4 } = \dfrac{ -6w - 6y }{ -6 }$ Solve for $w$.
Explanation: Multiply both sides by the left denominator. $\dfrac{ 7w + 7x }{ -{4} } = \dfrac{ -6w - 6y }{ -6 }$ $-{4} \cdot \dfrac{ 7w + 7x }{ -{4} } = -{4} \cdot \dfrac{ -6w - 6y }{ -6 }$ $7w + 7x = -{4} \cdot \dfrac { -6w - 6y }{ -6 }$ Multiply both sides by the right denominator. $7w + 7x = -4 \cdot \dfrac{ -6w - 6y }{ -{6} }$ $-{6} \cdot \left( 7w + 7x \right) = -{6} \cdot -4 \cdot \dfrac{ -6w - 6y }{ -{6} }$ $-{6} \cdot \left( 7w + 7x \right) = -4 \cdot \left( -6w - 6y \right)$ Distribute both sides $-{6} \cdot \left( 7w + 7x \right) = -{4} \cdot \left( -6w - 6y \right)$ $-{42}w - {42}x = {24}w + {24}y$ Combine $w$ terms on the left. $-{42w} - 42x = {24w} + 24y$ $-{66w} - 42x = 24y$ Move the $x$ term to the right. $-66w - {42x} = 24y$ $-66w = 24y + {42x}$ Isolate $w$ by dividing both sides by its coefficient. $-{66}w = 24y + 42x$ $w = \dfrac{ 24y + 42x }{ -{66} }$ All of these terms are divisible by $6$ Divide by the common factor and swap signs so the denominator isn't negative. $w = \dfrac{ -{4}y - {7}x }{ {11} }$